The complete energy expression of a deformed single-walled carbon nanotube (SWNT) is derived in the continuum limit from the local density approximation model proposed by Lenosky et al. [Nature (London) 355, 333 (1992)] and is shown to be consistent with the classic shell theory by which Young’s modulus, the Poisson ratio, and the effective wall thickness of SWNT’s are obtained as $Y=4.70\mathrm{}\hspace{0.5em}\mathrm{TPa},$ $\nu =0.34,$ and $h=0.75\mathrm{}\hspace{0.5em}\mathrm{\AA },$ respectively. The elasticity of a multiwalled carbon nanotube (MWNT) is investigated as the combination of the above SWNT’s of layer distance $d=3.4\mathrm{}\hspace{0.5em}\mathrm{\AA }$ and the effective Young’s modulus of the MWNT is found to be an apparent function of the number of layers, N, varying from 4.70 to 1.04 TPa for $N=1\mathrm{}$ to $\infty .$

• Received 18 December 2001

DOI:https://doi.org/10.1103/PhysRevB.65.233407